Torque Acting on a Magnetic Dipole in a Uniform Magnetic Field

Show that the orbital magnetic dipole moment of a revolving electron is `("evr")/2`

The work done for rotating a magnet with magnetic dipole moment m, through 90° from its magnetic meridian is n times the work done to rotate it through 60°. Find the value of n.

A magnetic needle placed in uniform magnetic field has magnetic moment of 2 x 10^-2 A·m², and a moment of inertia of 7 .2 x 10^-7 kg·m². It performs 10 complete oscillations in 6 s. What is the magnitude of the magnetic field?

A magnetic needle is suspended freely so that it can rotate freely in the magnetic meridian. In order to keep it horizontal position, a weight of 0.2 g is kept on one end of the needle. If the pole strength of the needle is 20 Am, find the value of the vertical component of the Earth's magnetic field.

A short bar magnet is placed in an external magnetic field of 700 gauss. When its axis makes an angle of 30° with the external magnetic field, it experiences a torque of 0.014 Nm. Find the magnetic moment of the magnet, and the work done in moving it from its most stable to the most unstable position.